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Successive Convex Relaxation Approach to Bilevel Quadratic Optimization Problems

  • Akiko Takeda
  • Masakazu Kojima
Chapter
Part of the Applied Optimization book series (APOP, volume 50)

Abstract

The bilevel quadratic optimization problem is an instance of a hierarchical decision process where the lower level constraint set is dependent on decisions taken at the upper level. By replacing the lower level problem by the corresponding KKT optimality condition, the entire problem is transformed into a single level yet non-convex quadratic optimization problem involving the complementarity condition. In this paper, we adopt the successive convex relaxation method given by Kojima and Tunçel for approximating a nonconvex feasible region. By further exploiting the special structure of the bilevel quadratic optimization problem, we present new techniques which enable the efficient implementation of the successive convex relaxation method for the problem. The performance of these techniques is tested in a number of problems, and compared with some other procedures.

Keywords

Bilevel Programming Nonconvex Quadratic Program Semi-Infinite LP Relaxation Reformulation-Linearization Technique Lift-and-Project Procedure 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Akiko Takeda
    • 1
  • Masakazu Kojima
    • 1
  1. 1.Department of Mathematical and Computing ScienceTokyo Institute of TechnologyJapan

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